Name___________________________________
AP Statistics
Chapter 8 Review – Multiple Choice
1. An airplane has a front and a rear door that are both
opened to allow passengers to exit when the plane lands.
The plane has 100 passengers seated. The number of
passengers exiting through the front door should have
A. a binomial distribution with mean 50.
B. a binomial distribution with 100 trials but success
probability not equal to 0.5.
C. a geometric distribution with p = 0.5.
D. a normal distribution with a standard deviation of 5.
E. none of the above.
2. A small class has 10 students. Five of the students are
male and five are female. I write the name of each student
on a 3-by-5 card. The cards are shuffled thoroughly and I
draw cards, one at a time, until I get a card with the name
of a male student. Let X be the number of cards I draw.
The random variable X has which of the following
probability distributions?
A. A binomial distribution with mean 5.
B. A binomial distribution with mean 10.
C. The geometric distribution with probability of
success 0.1.
D. The geometric distribution with probability of
success 0.5.
E. None of the above.
3. For which of the following counts would a binomial
probability model be reasonable?
A. The number of traffic tickets written by each police
officer in a large city during one month.
B. The number of hearts in a hand of five cards dealt
from a standard deck of 52 cards that has been
thoroughly shuffled.
C. The number of 7’s in a randomly selected set of five
random digits from a table of random digits.
D. The number of phone calls received in a one-hour
period.
E. All of the above.
4. To pass the time, a toll booth collector counts the number
of cars that pass through his booth until he encounters a
driver with red hair. Suppose we define the random
variable Y = the number of cars the collector counts until
he gets a red-headed driver for the first time. Is Y a
geometric random variable?
A. Yes – all conditions for the geometric setting are met.
B. No – “red-headed driver” and “non-red-headed
driver” are not the same as “success” and “failure”.
C. No – we can’t assume that each “trial” (that is, each
car) is independent of previous trials.
D. No – the number of trials is not fixed.
E. No – the probability of a driver being red-headed is
not the same for each trial.
Scenario 6-12
There are twenty multiple-choice questions on an exam,
each having responses a, b, c, or d. Each question is worth
five points and only one option per question is correct.
Suppose the student guesses the answer to each question,
and the guesses from question to question are
independent.
5. Use Scenario 6-12. The distribution of X = the number of
questions the student will get correct, is
A. binomial with parameters n = 5 and p = 0.2.
B. binomial with parameters n = 20 and p = 0.25.
C. binomial with parameters n = 5 and p = 0.25.
D. binomial with parameters n = 4 and p = 0.25.
E. none of these.
6. Use Scenario 6-12. Which of the following expresses the
probability that the student gets no questions correct?
A.
B.
C.
D.
E.
7. In a certain game of chance, your chances of winning are
0.2. If you play the game five times and outcomes are
independent, which of the following represents the
probability that you win at least once?
A.
B.
C.
D.
E.
+
Scenario 6-13
A survey asks a random sample of 1500 adults in Ohio if
they support an increase in the state sales tax from 5% to
6%, with the additional revenue going to education. Let X
denote the number in the sample that say they support the
increase. Suppose that 40% of all adults in Ohio support
the increase.
8. Use Scenario 6-13. Which of the following is the mean 
of X?
A. 5%
B. 360
C. 0.40
D. 600
E. 90
9. Use Scenario 6-13. Which of the following is the
approximate standard deviation  of X ?
A. 0.40
B. 0.24
C. 19
D. 360
E. 9.20
Scenario 6-14
A worn out bottling machine does not properly apply caps
to 5% of the bottles it fills.
10. Use Scenario 6-14. If you randomly select 20 bottles from
those produced by this machine, what is the approximate
probability that exactly 2 caps have been improperly
applied?
A. 0.0002
B. 0.19
C. 0.74
D. 0.81
E. 0.92
C. 40
D. 50
E. 80
13. Use Scenario 6-14. In a production run of 800 bottles,
what is the standard deviation for the number of bottles
with improperly applied caps?
A. 1.38
B. 6.16
C. 6.32
D. 6.89
E. 8.72
14. A college basketball player makes 80% of her free
throws. At the end of a game, her team is losing by two
points. She is fouled attempting a three-point shot and is
awarded three free throws. Assuming free throw attempts
are independent, what is the probability that she makes at
least two of the free throws?
A. 0.896.
B. 0.80.
C. 0.64.
D. 0.512.
E. 0.384.
15. A college basketball player makes 5/6 of his free throws.
Assuming free throw attempts are independent, the
probability that he makes exactly three of his next four
free throws is
A.
.
B.
.
C.
.
11. Use Scenario 6-14. If you randomly select 20 bottles from
those produced by this machine, what is the approximate
probability that between 2 and 6 (inclusive) caps have
been improperly applied?
A. 0.19
B. 0.26
C. 0.38
D. 0.74
E. 0.92
12. Use Scenario 6-14. In a production run of 800 bottles,
what is the expected value for the number of bottles with
improperly applied caps?
A. 4
B. 8
D.
.
E.
.
16. Roll one 8-sided die 10 times. The probability of getting
exactly 3 sevens in those 10 rolls is given by
A.
B.
Scenario 6-15
Suppose that 40% of the cars in a certain town are white.
A person stands at an intersection waiting for a white car.
Let X = the number of cars that must drive by until a white
one drives by.
C.
20. Use Scenario 6-15.
D.
A.
B.
C.
D.
E.
E.
17. The binomial expression
gives the
probability of
A. at least 2 successes in 8 trials if the probability of
success in one trial is 1/3.
B. at least 2 successes in 8 trials if the probability of
success in one trial is 2/3.
C. exactly 2 successes in 8 trials if the probability of
success in one trial is 1/3.
D. exactly 2 successes in 8 trials if the probability of
success in one trial is 2/3.
E. at least 6 successes in 8 trials if the probability of
success in one trial is 2/3.
18. A college basketball player makes 80% of her free
throws. Suppose this probability is the same for each free
throw she attempts, and free throw attempts are
independent. The probability that she makes all of her
first four free throws and then misses her fifth attempt this
season is
A. 0.32768.
B. 0.08192.
C. 0.06554.
D. 0.00128.
E. 0.00032.
19. A college basketball player makes 80% of her free
throws. Suppose this probability is the same for each free
throw she attempts, and free throw attempts are
independent. The expected number of free throws
required until she makes her first free throw of the season
is
A. 2.
B. 1.25.
C. 0.80.
D. 0.31.
E. 0.13
=
0.0518
0.1296
0.2592
0.8704
0.9482
21. Use Scenario 6-15. The expected value of X is:
A. 1
B. 1.5
C. 2
D. 2.5
E. 3
Scenario 6-16
A poll shows that 60% of the adults in a large town are
registered Democrats. A newspaper reporter wants to
interview a local democrat regarding a recent decision by
the City Council.
22. Use Scenario 6-16. If the reporter asks adults on the street
at random, what is the probability that he will find a
Democrat by the time he has stopped three people?
A. 0.936
B. 0.216
C. 0.144
D. 0.096
E. 0.064
23. Use Scenario 6-16. On average, how many people will the
reporter have to stop before he finds his first Democrat?
A. 1
B. 1.33
C. 1.67
D. 2
E. 2.33
Scenario 6-17
You are stuck at the Vince Lombardi rest stop on the New
Jersey Turnpike with a dead battery. To get on the road
again, you need to find someone with jumper cables that
connect the batteries of two cars together so you can start
your car again. Suppose that 16% of drivers in New
Jersey carry jumper cables in their trunk. You begin to
ask random people getting out of their cars if they have
jumper cables.
24. Use Scenario 6-17. On average, how many people do you
expect you will have to ask before you find someone with
jumper cables?
A. 1.6
B. 2
C. 6
D. 6.25
E. 16
25. Use Scenario 6-17. You’re going to give up and call a tow
truck if you don’t find jumper cables by the time you’ve
asked 10 people. What’s the probability you end up
calling a tow truck?
A. 0.8251
B. 0.1749
C. 0.1344
D. 0.0333
E. 0.0280
26. At a school with 600 students, 25% of them walk to
school each day. If we choose a random sample of 40
students from the school, is it appropriate to model the
number of students in our sample who walk to school with
a binomial distribution where n = 40 and p = 0.25?
A. No, the appropriate model is a geometric distribution
with n = 40 and p = 0.25.
B. No, it is never appropriate to use a binomial setting
when we are sampling without replacement.
C. Yes, because the sample size is less than 10% of the
population size.
D. Yes, because
and n < 30.
E. We can’t determine whether a binomial distribution
is appropriate unless the number of trials is known.
27. A jar has 250 marbles in it, 40 of which are red. What is
the largest sample size we can take from the jar (without
replacement) if we want to use the binomial distribution
to model the number of red marbles in our sample?
A. 50
B. 40
C. 25
D. 4
E. You can’t use a binomial distribution in this setting.
Chapter 8 Review
Answer Section
MULTIPLE CHOICE
1. ANS: E
PTS:
1
TOP:
Binomial/Geometric setting
2. ANS: E
PTS:
1
TOP:
Binomial/Geometric setting
3. ANS: C
PTS:
1
TOP:
Binomial setting
4. ANS: A
PTS:
1
TOP:
Geometric setting
5. ANS: B
PTS:
1
TOP:
Binomial setting
6. ANS: B
PTS:
1
TOP:
Binomial probability
7. ANS: C
PTS:
1
TOP:
Binomial probability
8. ANS: D
PTS:
1
TOP:
Binomial mean
9. ANS: C
PTS:
1
TOP:
Binomial standard deviation
10. ANS: B
PTS:
1
TOP:
Binomial probability
11. ANS: B
PTS:
1
TOP:
Binomial probability
12. ANS: C
PTS:
1
TOP:
Binomial mean
13. ANS: B
PTS:
1
TOP:
Binomial standard deviation
14. ANS: A
PTS:
1
TOP:
Binomial probability
15. ANS: E
PTS:
1
TOP:
Binomial probability
16. ANS: B
PTS:
1
TOP:
Binomial probability
17. ANS: C
PTS:
1
TOP:
Binomial probability
18. ANS: B
PTS:
1
TOP:
Geometric probability
19. ANS: B
PTS:
1
TOP:
Geometric mean
20. ANS: D
PTS:
1
TOP:
Geometric probability
21. ANS: D
PTS:
1
TOP:
Geometric mean
22. ANS: A
PTS:
1
TOP:
Geometric probability
23. ANS: C
PTS:
1
TOP:
Geometric mean
24. ANS: D
PTS:
1
TOP:
Geometric probability
25. ANS: B
PTS:
1
TOP:
Geometric mean
26. ANS: C
PTS:
1
TOP:
Binomial setting and sampling
27. ANS: C
PTS:
1
TOP:
Binomial setting and sampling